Search Results for ""

Tutte's fragment (Taylor 1997) is the 15-node graph illustrated above (Grünbaum 2003, pp. 358-359 and Fig. 17.1.3). If the graph obtained by adding pendant edges to corners ...

The disorder number of a simple connected graph on n vertices is defined as the maximum length of a walk along the edges of the graph taken over all ordering of its vertices ...

A forest is an acyclic graph (i.e., a graph without any graph cycles). Forests therefore consist only of (possibly disconnected) trees, hence the name "forest." Examples of ...

The Moser spindle is the 7-node unit-distance graph illustrated above (Read and Wilson 1998, p. 187). It is sometimes called the Hajós graph (e.g., Bondy and Murty 2008. p. ...

Given an undirected graph, a degree sequence is a monotonic nonincreasing sequence of the vertex degrees (valencies) of its graph vertices. The number of degree sequences for ...

The detour index omega(G) of a graph G is a graph invariant defined as half the sum of all off-diagonal matrix elements of the detour matrix of G. Unless otherwise stated, ...

A Hamilton decomposition (also called a Hamiltonian decomposition; Bosák 1990, p. 123) of a Hamiltonian regular graph is a partition of its edge set into Hamiltonian cycles. ...

The quadratic embedding constant QEC(G) of a finite simple connected graph G on n vertices is defined as the maximum of the product vDv over all real n-vectors v satisfying ...

The chromatic invariant theta(G) of a connected graph G is the number of spanning trees of G that have internal activity 1 and external activity 0. For graphs other than the ...

A set of graph vertices A of a graph with graph edges V is independent if it contains no graph edges.